If the area of a rectangle with width \( x \) can be represented with the expression \( A(x)=x(14-x) \), what is the perimeter of the rectangle?

To find the perimeter of the rectangle, we start by identifying the dimensions from the area expression \( A(x) = x(14 - x) \), which implies the length is \( 14 - x \) and the width is \( x \). The formula for the perimeter \( P \) of a rectangle is given by \( P = 2 \times (length + width) \). Thus, substituting the dimensions gives us: \[ P = 2 \times (x + (14 - x)) = 2 \times 14 = 28. \] So the perimeter of the rectangle is 28 units. Now, let's explore the exciting world of rectangles! In the realm of ancient geometry, the rectangle has always been a favorite among mathematicians, dating back to the time of Euclid around 300 BC. The properties of rectangles were studied extensively, leading to fundamental concepts in mathematics today, including the Pythagorean theorem! Need some problem-solving magic? When working with rectangles, it's crucial to remember that the area and perimeter are just two pieces of a bigger puzzle. A common mistake is forgetting to consider that changes to one dimension will affect the other. For example, if you increase width \( x \), remember to check how it impacts the length \( 14 - x \). Always keep the relationship in mind to master your rectangle calculations!